Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 4x - 3$ and $ JT = 7x - 18$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {4x - 3} = {7x - 18}$ Solve for $x$ $ -3x = -15$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 4({5}) - 3$ $ JT = 7({5}) - 18$ $ CJ = 20 - 3$ $ JT = 35 - 18$ $ CJ = 17$ $ JT = 17$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {17} + {17}$ $ CT = 34$